Post-Stack inversion of reflection data in seismic exploration can be used to obtain detailed information about lithology variations in the zone of interest. Generalized Linear Inversion (GLI) has previously been applied as a useful tool to achieve this. The purpose of my investigation is to apply GLI to data from the Coal Measures. It is known that in the Coal Measures the most strongly reflecting horizons are the coal seams, which are the exploration targets. In the seismic bandwidth they are thin beds, which causes particular problems associated with vertical resolution for the inversion. The method is applied to a seismic line from the Belvoir Coalfield supplied by British Coal. In order to get better relative amplitudes and to keep the same bandwidth down the whole section, the data were carefully reprocessed using the ProMAX software. Wireline log data from two boreholes intersected by the seismic line were edited to generate acoustic impedance logs as functions of time. Software was developed to implement GLI, and tested on synthetic data before applying it to the reprocessed data. The initial guesses for earth and wavelet models at the boreholes were obtained after systematic studies to determine the best strategy. The construction of the initial guess for the boundary locations elsewhere on the section is very critical for the success of the search for the global minimum. A combination of structural interpretation and the inversion results obtained from the previous trace was found to do the best job. I have tried to invert separately for the boundary locations, acoustic impedances and the wavelet, with the wavelet parameterized in the frequency domain. I found that, provided that the wavelet extracted at a borehole is a good estimate with low error energy, the most successful strategy is just to invert for the boundary locations, keeping the acoustic impedances and the extracted wavelet fixed. If the extracted wavelet is not a good estimate, then parameterizing the wavelet in the frequency domain and optimizing those parameters at the borehole is a useful approach. None of the implemented inversion strategies produced a perfect result. Discrepancies were due to the difficulty in obtaining true relative amplitude values on the processed section. The inversion results and systematic studies on the field dataset indicate that the assumptions of the convolutional model are not satisfied by the processed section.